Faraday's Law with Calculus Video Lessons

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# Problem: A (17cm × 17cm) square loop lies in the xy plane. The magnetic field in this region of space is B = (0.31t î + 0.55t2 k̂)T where t is in seconds.1) What is the induced emf in the loop at 0.5 s?2) What is the induced emf in the loop at 1.0 s?Express your answer to two significant figures and include the appropriate units.

###### FREE Expert Solution

Induced emf:

$\overline{){\mathbf{\epsilon }}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{d}{\mathbf{\varphi }}_{\mathbf{B}}}{\mathbf{d}\mathbf{t}}}$

Power rule of derivation,

$\overline{)\frac{\mathbit{d}}{\mathbit{d}\mathbit{t}}\mathbf{\left(}{\mathbit{t}}^{\mathbit{n}}\mathbf{\right)}{\mathbf{=}}{\mathbit{n}}{{\mathbit{t}}}^{\mathbit{n}\mathbf{-}\mathbf{1}}}$

$\overline{){{\mathbf{\varphi }}}_{{\mathbf{B}}}{\mathbf{=}}\stackrel{\mathbf{⇀}}{\mathbf{B}}{\mathbf{·}}\stackrel{\mathbf{⇀}}{\mathbf{A}}}$

B = (0.31t i + 0.55t2 k)T

A = (0.17 m × 0.17 m) k = (0.0289 m2) k (The area is perpendicular to the z-plane

${{\mathbf{\varphi }}}_{{\mathbf{B}}}$= (0.31t i + 0.55t2 k)•(0.0289 m2) k = (0.55t2 k)•(0.0289) k = 0.015895t2 T•m2

1)

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###### Problem Details

A (17cm × 17cm) square loop lies in the xy plane. The magnetic field in this region of space is B = (0.31t î + 0.55t2 k̂)T where t is in seconds.

1) What is the induced emf in the loop at 0.5 s?

2) What is the induced emf in the loop at 1.0 s?

Express your answer to two significant figures and include the appropriate units.